We have continued to elaborate our comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster (tens of seconds) oscillations stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower (five minutes) oscillations stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The latter, notably, are a first-line target of insulin-stimulating drugs, such as the sulfonylureas (tolbutamide, glyburide) used in the treatment of Type 2 Diabetes. The model thus consists of an electrical oscillator (EO) and a metabolic (glycolytic) oscillator (G)) and is referred to as the Dual Oscillator Model (DOM). See Ref. # 1 for a recent review. We have used a simplified model consisting only of the EO to explain the behavior of a mouse model for familial hyperinsulinism, in which is most commonly associated with impaired or reduced number of K(ATP) channels (Ref. # 5). In the absence of this major inhibitory mechanism, the islets secrete insulin inappropriately even when plasma glucose is not elevated, resulting in chronic hypoglycemia. The mouse model we investigated is the Kir6.2AAA mutant, in which 2/3 of the cells in an islet contain only mutant AAA channels and the rest contain normal channels. In spite of this overall 2/3 decrease in K(ATP) conductance, the glucose dose response curve is only shifted about 2 mM; the threshold for electrical activity that can lead to insulin secretion is shifted from about 6 mM glucose to about 4 mM. The model indicates that this is because the increased electrical activity raises cytosolic calcium, which inhibits ATP production in the mitochondria and opens a greater fraction of the available K(ATP) channels than in wild-type animals. Thus the mutant animals compensate for the reduced number of K(ATP) channels by using the remnant more efficiently. We have previously described a heuristic diagrammatic model that shows how the two oscillators combine to produce the diverse patterns exhibited by islets. In the current year, developed a new mathematical tool to translate the diagrammatic representation into a mathematical form (Ref. # 2). This is done by overlapping the bifurcation diagrams for the two oscillators (OBD method). This is possible because calcium is an output of the EO and in input of the GO and ATP is an output of the GO and an input of the EO. The OBD makes finer distinctions than the diagrammatic approach and also reveals new insights. For example, it shows that the EO is not simply driven by the GO but also feeds back. The dominance of one or the other depends on the conditions (and hence the parameters of the model). Of particular, interest, we find that the most typical case is for the two oscillators to share control, exchanging dominance in different phases of the oscillation. We speculate that this situation, which was unexpected during model development, may optimize the ability of the islet to integrate metabolic and electrical signals. A further mathematical development is the use of homogenization theory to derive a continuous representation of the islets by partial differential equations instead of a discrete representation in terms of point cells connected by resistors (Ref. # 3). The membrane potential, cytosolic calcium, and endoplasmic reticulum calcium are each represented as a continuous concentration field. This extends similar work with two concentration fields used in studying non-electrical calcium oscillations and cardiac electrical activity. In addition to the dynamics of calcium, secretion of insulin depends on the dynamics of the insulin-containing granule themselves. The latter are found in several distinct pools within the beta-cell, including a very large reserve pool in the cytosol (more than 10,000 granules), a pool of granules docked at the plasma membrane but not release ready (about 600 granules), a primed pool that is available for release whenever elevated calcium is encountered (about 50 granules), and a pool that is tethered in close proximity to calcium channels and hence the most strongly affected by calcium channel openings (about 10 granules). A comprehensive model was developed, combining elements of the classic, phenomenological Grodsky model, dating from the 1960's, with recent data tracking the movements of granules via capacitance or imaging techniques. The Grodsky model was very successful in accounting for the time course of first and second phase insulin release (over 10 minute and 60 minute time scales, respectively), whereas the granule measurements have looked at secretion on time scale of milliseconds and seconds. Moreover, the Grodsky model was developed before much was known about the role of calcium rise in response to glucose-induced closure of K(ATP) channels, and glucose was therefore the only input to the model. Thus, it was unable to account for later experiments in which the effects of glucose metabolism aand calcium rise were dissociated. Last your we developed a new model that provided a view of the main phenomena on the full range of time scales from less than one second to one hour. In the current periods, we have extended the model (Ref. # 4) to take into account new data suggesting that there are two classes of vesicles, vesicles with low affinity for calcium that need to be tethered to calcium channels, and a new class with high affinity for calcium that response to bulk cytosolic calcium. The model predicts that the high affinity vesicles represent the same pool identified in separate experiments as newcomer vesicles that arrive at the plasma membrane and are rapidly released during the second phase of insulin secretion, whereas the vesicles associated with calcium channels are the pre-resident vesicles that predominate during first-phase secretion. This arrangement may allow beta-cells to conserve the low affinity pool for responding to sudden glucose increases.